Question: Simplify. Remove all perfect squares from inside the square root. $\sqrt{112a^6}=$
Solution: Factor $112$ and find the greatest perfect square: $112=2\cdot 2\cdot 2\cdot 2\cdot 7=4^2\cdot 7$ Find the greatest perfect square in $a^6$ : $a^6=\left(a^3\right)^2$ $\begin{aligned} \sqrt{112a^6}&=\sqrt{4^2\cdot 7\cdot \left(a^3\right)^2} \\\\ &=\sqrt{4^2}\cdot \sqrt{7} \cdot \sqrt{\left(a^3\right)^2} \\\\ &=4\cdot \sqrt{7} \cdot a^3 \\\\ &=4a^3\sqrt{7} \end{aligned}$